An analytical model for estimating the force and displacement of fully grouted rock bolts. (January 2020)

• Record Type: Journal Article
• Authors: Zhang, Weili; Huang, Lei; Juang, C. Hsein
• Is Part Of: Computers and geotechnics. Volume 117(2020)
• Publication Date: 2020-01
• Subjects: Pull-out test -- Changing load -- Analytical model -- Interface -- Shear stress -- Fully grouted rock bolt; τ Shear stress at the bolt-grout interface -- τr Residual shear strength of the rock bolt -- τu Peak shear strength of the rock bolt -- τ' Shear stress of the rock bolt at the end point of the elastic-plastic part -- τ0 Shear stress at the bolt-grout interface at the loading end -- ω Ratio of τr to τu -- σ Axial stress of the rock bolt -- σ0 Axial stress of the rock bolt at the loading end -- F Axial force of the rock bolt -- F0 Axial force of the rock bolt at the loading end -- Fcr Critical axial force during the debonding stage -- Fu Ultimate load of the rock bolt -- s Displacement of the rock bolt -- s0 Displacement of the rock bolt at the loading end -- Eb Young's modulus of the rock bolt -- Em Young's modulus of the rock mass -- Eg Young's modulus of the grout -- Gm Shear modulus of the rock mass -- Gg Shear modulus of the grout -- μm Poisson's ratio of the rock mass -- μg Poisson's ratio of the grout -- k Shear stiffness -- rb Radius of the rock bolt -- rg Radius of the grout -- β An introduced parameter, β=2krbEb -- l Length of the rock bolt -- R Radius of the rock bolt influenced -- x Distance from the loading end -- x0 Coordinate of the end point of residual strength of the rock bolt -- x1 Coordinate of the position of the shear stress equal to τu -- a Length of the bolt, a = x1 − x0; Engineering geology -- Data processing -- Periodicals; Soil mechanics -- Data processing -- Periodicals; Rock mechanics -- Data processing -- Periodicals; 624.1510285
• DOI: 10.1016/j.compgeo.2019.103222
• Languages: English
• ISSNs: 0266-352X

Abstract

Abstract: Previously proposed models for estimating the force and displacement of fully grouted rock bolts rarely describe the variations in shear stress and axial force in response to a changing load. In this work, an analytical model considering this variation pattern is developed. The model makes two assumptions: (I) failure occurs at the bolt-grout interface, and (II) the shear stiffness is constant along this interface. First, according to the variation in interfacial stress, the complete rock bolt deformation process is divided into three stages: (1) the elastic stage, (2) the softening stage, and (3) the debonding stage. Equations for axial force and displacement during each stage are derived under the two assumptions. Using these equations, the developed model accommodates the three stages. The model estimates of force and displacement show good agreement with pull-out test observations, indicating that the model effectively describes the complete rock bolt deformation process during a pull-out test. However, one limitation of the proposed model is that, for simplification, as in most related models, the radial stress along the bolt is not considered.